In the CI-NEB method, the minimum energy path (MEP) connecting the initial and final states is determined by searching for the path where the spring force between adjacent image configurations only points along the tangent direction of this path. The maxima on the MEP are saddle points on the energy landscape with zero first derivative of the reaction coordinate, and the energy of the highest saddle point minus the energy of the initial state gives \(\Delta E_{\text{a}}\)  [1]}, [2]}. For all CI-NEB calculations that we performed with different model Al alloys, the MEPs are simple: each MEP only has one maximum at the transition state with two local minima corresponding to the initial and final states, respectively. The relative distance between the initial and final states along the MEP, \(D_{\text{MEP}}\) , is a natural choice for the reaction coordinate. The sign of \(D_{\text{MEP}}\)  is positive if the states migrate from the initial to the final and negative if the states migrate from the final to the initial states. The magnitude of \(D_{\text{MEP}}\)  is defined as the length of the high-dimensional curvature of the MEP as follows:
\(D_{\text{MEP}} = \int \limits _{\text{MEP}} {ds} = \lim \limits _{N\rightarrow \infty } \sum \limits _{j=0}^{N}D_{\text{RHD}}(I_{j}, I_{j+1})\) 
